Convex semigroups on Lp-like spaces

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DENK, Robert, Michael KUPPER, Max NENDEL, 2021. Convex semigroups on Lp-like spaces. In: Journal of Evolution Equations. Springer. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-021-00693-3

@article{Denk2021Conve-53493, title={Convex semigroups on Lp-like spaces}, year={2021}, doi={10.1007/s00028-021-00693-3}, issn={1424-3199}, journal={Journal of Evolution Equations}, author={Denk, Robert and Kupper, Michael and Nendel, Max} }

eng terms-of-use Kupper, Michael 2021-04-27T07:07:01Z Convex semigroups on L<sup>p</sup>-like spaces 2021 2021-04-27T07:07:01Z In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having L<sup>p</sup>-spaces in mind as a typical application. We show that the basic results from linear C<sub>0</sub>-semigroup theory extend to the convex case. We prove that the generator of a convex C<sub>0</sub>-semigroup is closed and uniquely determines the semigroup whenever the domain is dense. Moreover, the domain of the generator is invariant under the semigroup, a result that leads to the well-posedness of the related Cauchy problem. In a last step, we provide conditions for the existence and strong continuity of semigroup envelopes for families of C<sub>0</sub>-semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations. Denk, Robert Denk, Robert Kupper, Michael Nendel, Max Nendel, Max

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